Related papers: A note on fractional derivative modeling of broadb…
We explain how to encode the essential data of a PDE on jet bundle into a more intrinsic object called Pfaffian fibration. We provide motivations to study this new notion and show how prolongations, integrability and linearisations of PDEs…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
Metasurface based super absorbers exhibit near unity absorbance. While the absorption peak can be tuned by the geometry/size of the sub-wavelength resonator, broadband absorption can be obtained by placing multiple resonators of various…
Photonic crystals enable fine control over light propagation at the nanoscale, and thus play a central role in the development of photonic and quantum technologies. Photonic band diagrams (BDs) are a key tool to investigate light…
We introduce complex order fractional derivatives in models that describe viscoelastic materials. This can not be carried out unrestrictedly, and therefore we derive, for the first time, real valued compatibility constraints, as well as…
We present three schemes for the numerical approximation of fractional diffusion, which build on different definitions of such a non-local process. The first method is a PDE approach that applies to the spectral definition and exploits the…
The frequency-dependent conductivity is studied for the one-dimensional Hubbard model, using a selection rule, the Bethe ansatz, and symmetries associated with conservation laws. For densities where the system is metallic the absorption…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
Distributed-order time-fractional wave equations appear in the modeling of wave propagation in viscoelastic media. The material characteristics of the medium are modeled through constitutive functions or distributions in the…
In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying…
We have proposed and developed a method to utilize attosecond pulses in diffraction imaging techniques applied to complex samples. In this study, the effects of the broadband properties of the wavefield owing to attosecond pulses are…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
In this article an upscaled model is presented, for complex networks with highly clustered regions exchanging some abstract quantities in both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open…
This work theoretically analyzes the sound absorption properties of a chirped multi-layer porous material including transmission, in particular showing the broadband unidirectional absorption properties of the system. Using the combination…
The employment of nonlocal PDE models to describe biological aggregation and other phenomena has gained considerable traction in recent years. For cell populations, these methods grant a means of accommodating essential elements such as…
In this article we consider the approximation of a variable coefficient (two-sided) fractional diffusion equation (FDE), having unknown $u$. By introducing an intermediate unknown, $q$, the variable coefficient FDE is rewritten as a lower…
Broadband ferromagnetic resonance (bbFMR) spectroscopy is an established experimental tool to quantify magnetic properties. Due to frequency-dependent transmission of the microwave setup, bbFMR measurements in the frequency domain require a…
The Debye-Falkenhagen differential equation is commonly used as a mean-field macroscopic model for describing electrochemical ionic drift and diffusion in dilute binary electrolytes when subjected to a suddenly applied potential smaller…
A parallel dispersive finite-difference time-domain (FDTD) method for the modeling of three-dimensional (3-D) electromagnetic cloaking structures is presented in this paper. The permittivity and permeability of the cloak are mapped to the…
In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…